What are the divisors of 8236?

1, 2, 4, 29, 58, 71, 116, 142, 284, 2059, 4118, 8236

There is a total of 12 positive divisors.
The sum of these divisors is 15120.
The arithmetic mean is 1260.

8 even divisors

2, 4, 58, 116, 142, 284, 4118, 8236

4 odd divisors

1, 29, 71, 2059

How to compute the divisors of 8236?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 8236 by each of the numbers from 1 to 8236 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

8236 / 1 = 8236 (the remainder is 0, so 1 is a divisor of 8236)
8236 / 2 = 4118 (the remainder is 0, so 2 is a divisor of 8236)
8236 / 3 = 2745.3333333333 (the remainder is 1, so 3 is not a divisor of 8236)
...
8236 / 8235 = 1.0001214329083 (the remainder is 1, so 8235 is not a divisor of 8236)
8236 / 8236 = 1 (the remainder is 0, so 8236 is a divisor of 8236)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 8236 (i.e. 90.752410436307). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

8236 / 1 = 8236 (the remainder is 0, so 1 and 8236 are divisors of 8236)
8236 / 2 = 4118 (the remainder is 0, so 2 and 4118 are divisors of 8236)
8236 / 3 = 2745.3333333333 (the remainder is 1, so 3 is not a divisor of 8236)
...
8236 / 89 = 92.539325842697 (the remainder is 48, so 89 is not a divisor of 8236)
8236 / 90 = 91.511111111111 (the remainder is 46, so 90 is not a divisor of 8236)